Rapid calculation of the periodic steady state for electronically switched, time varying power system loads

The periodic steady state of power distribution system loads is studied for electronically switched, time varying cases. Many loads of this type appear on contemporary power systems as energy saving and controllable demands. Several alternative methods of calculating the periodic steady state are discussed and a new method is proposed based on the frequency modulation property of the discrete Fourier transform. The new method is termed the gain-shift formula (GSF) because the format of the technique entails adding frequency shifted terms which represent the parameter to be calculated. An example of a triac-switched load on the distribution system is given. The main advantages of the GSF are: rapid calculation of the periodic steady state; and efficient calculation of the frequency spectrum of voltages and currents in the periodic steady state.